Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
156 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #4505 | C2 | semidirect |
| 5. #4504 | C2 | semidirect |
| 10. C3×M32 | C4 | semidirect |
| 34. C3×C16 | C2×C4 | semidirect |
| 38. M32 | Dic3 | semidirect |
| 69. C16 | C2×Dic3 | semidirect |
| 106. C3 | #2159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×M32 | 2 |
| #5106 | 2 |
| C2×#818 | 2 |
| #4505 | 2 |
| #4504 | 2 |
| #2159 | 3 |